Investigation of scattering from soundproof single sphere under external influence

The scattering from a single soundproof sphere is investigated during the passage of two types of waves: a spherical wave from a monopole radiation source and a plane wave. In solving the Helmholtz equation, a numerical technique based on the fast method of multipoles is used, which allows achieving high accuracy of the results obtained, and also minimizing computer time. The calculations are compared with known experimental data and a good agreement is obtained. Formulas are obtained for the main characteristic of the scattering field (the total scattering cross-section) for a sphere with an arbitrary acoustic impedance. Its dependence on the main parameters of the "sphere — environment" system for two kinds of the incident field is shown. A numerical parametric analysis of the value of the potential on the surface of a sphere for different values of its radius, complex impedance, the type of external influence, etc.